Digital Synthesis

Even though they look a lot like pianos, every digital synthesizer
is a computer. There are many types of synthesis advertised, but
when the hype and marketing prose is translated into English,
we discover they all work more or less the same way. Like CD players,
digital synthesizers produce a stream of numbers at a steady sample
rate, which are converted to analog form to drive speakers and
produce sound. Everything we have learned about digital recording
(Nyquist frequency, anti-alias filters and so forth) applies to
digital synthesis.

A digital synthesizer has the same functions as a modular analog
synthesizer. But instead of circuitry, each module is a subroutine
within the main synthesis program. This program is essentially
a loop that repeats once for each output sample. The subroutines
must each be executed at least once per sample period, and many
of them must execute once per note per sample period. Thus the
number of notes that may be played, and the complexity of the
sound available is determined by the speed of the CPU. As with
personal computers, the faster CPUs are the most expensive, and
this is reflected in the cost of the instrument.

The cost can be cut down by using a slow sample rate, but this
is easily audible in the sound of the instrument. A state of the
art synthesizer meets CD quality standards.

This is the typical signal flow, the digital equivalent of
the patch:

The three top boxes represent processes that deal directly
with the signal and must be executed at top speed. Control processes
may be updated at a more comfortable rate, so it is less expensive
to add a second LFO to all voices than it is to add a second signal
generator.

Signal Generation: Wavetables

The heart of any signal generation routine is Wavetable lookup.
A wavetable is a section of memory that contains a representation
of a segment of sound. This may be as simple as a single cycle
of sine wave, or may be a complete recording of a traditional
instrument playing a note. On each sample period a value is taken
from the wavetable and sent to the output. If the sample rate
of the synthesizer is the same as that used for the initial recording,
the pitch produced will be the same. In the case of a single cycle
wavetable, the frequency produced will be the sample rate divided
by the number of entries in the table.

To produce a continuous tone, the table is read over and over.

To play other pitches, the values in the table are taken out
of order. If every other value is output, the frequency is doubled.
To go down an octave, each value could be used twice, but that
would distort the wave noticeably. Modern instruments calculate
a value that would fall between the entries in the table, a process
called interpolation. Sophisticated interpolation routines can
produce any pitch desired, including smooth glissandi and pitchbends.

Interpolation is the most time consuming process within the
program loop, so the number of tones you can play this way is
going to be limited in a particular instrument. This will then
determine the maximum number of notes possible, depending on how
many tones are used to create a note.

Variation of tone

Wavetable synthesis has one serious drawback, a very static
spectrum of the sound. Most real instruments produce dynamic spectra
that change over the duration of a note and never repeat in quite
the same way. Simple wavetable gives the sound of a toy organ,
occasionally useful, but basically boring. To get around this
a variety of strategies can be found:

Very Large Wavetables

Essentially, there is enough sound in the wavetable to play
an entire note on one pass, or at least to loop with a moderately
long period that sounds like vibrato. Most often, these class
of synthesizers use recordings of traditional instruments as the
wavetable content. You may be limited to a particular set of recordings,
or you may be able to make your own. These are the ubiquitous
samplers and sample playback units. Sampling was first marketed
by E-mu, and they have a wide range of instruments based upon
the technique, but nearly every instrument on the market today
has some recorded samples in it.

Frequency Modulation

We learned on the modular synthesizer how to create dynamic
sounds with the simple trick of using one oscillator to modulate
the frequency of another. In a digital system this can be done
with elegance and control. The sounds are not inherently "natural"
in the sense of sounding like traditional instruments, but a few
realistic efforts exist. For sounds with a vibrancy and life of
their own, the technique is unsurpassed. The Yamaha corporation
had a patent on FM, and even though that patent has run out, few
other manufacturers are interested in pursuing it.

Waveshaping

Waveshaping adds a step of deliberate distortion to a wavetable
type generator. Usually this is accomplished by the simple expedient
of using the output of the wavetable routine to find a value in
a table that contains some strange transfer function. It's quick
and cheap, and if the wavetable output is added to some slowly
changing value before the lookup process the sound can be made
to evolve over time.

Modeling

The newest wrinkle in synthesis is Physical Modeling. In this
scheme, the software is designed to recreate the actual behavior
of the instrument. For instance to model a flute, you would design
a subroutine that solves the equations describing the pressure
variance at the blowhole. These equations would be based on (among
other things) the breath pressure, the angle of inflow, and the
back pressure from the rest of the instrument. That result would
become a factor in the second subroutine, which may solve the
equation of the resonance of the head joint. The result of that
is both passed on to subroutines involving the body of the flute,
and fed back to the next iteration of the blowhole subroutine.
Results of the body resonance calculation likewise affect the
calculations for the head joint. In this way, the entire system
is interlinked just like a real flute.

To voice such a model, you specify the inflow angle and breath
pressure and the open or closed state of all the keys. Modeling
is very demanding of processor time, so the instruments that are
just coming to market are mostly monophonic. (I find it interesting
that one of the best selling of these models old fashioned analog
synthesizers!)

Combination Techniques

Most synthesizers allow you to make layers of tones with a
dynamically changing mix. This can create enough spectral variation
to get by in complex arrangements. Roland's technique of starting
with the attack of a recorded instrument and cross fading to a
simple waveform for the sustaining part of the note is very popular.
Emu allows the balance between two samples to be controlled by
the key velocity, which reduces exact repetition of sounds. Yamaha
even combines recorded samples with FM in several of its models.

Voice Level Processing

As on the analog synthesizer, generation of sound is only the
beginning of the process. The sound must be shaped, in both amplitude
and spectrum. To do this, the digital equivalents of Amplifiers
and filters are used. The old terminology of VCA and VCF remains
as DCA or TVCA (Digital Controlled Amplifier, Time Variant Amplifier)
and so on. These are controlled by other familiar items, Envelope
Generators and Low Frequency Oscillators. The more esoteric processors
such as Ring Modulators are rare, but do turn up occasionally.
There is little computation involved in amplifiers, LFOs or envelopes,
so the complexity offered is usually determined by the sophistication
of the user interface or marketing considerations. Filters are
another story.

Analog filters hung on in synthesizers long after everything
else had become digital. That is because a digital filter is computationally
complex, and programming them was not well understood. That has
changed. Recent models have very clean and flexible filters ranging
from simple low pass to the 14 pole morphing filters found in
the UltraProteous. Complex filters are usually implemented in
a second processor, and require a large section of memory, so
they do run up the cost of a machine, but as with analog synths,
a good filter can make up for a lot of deficiencies in the sound
generator.

Putting all this together, you get an instrument architecture
of some sort. This one is typical (JD-990):

You will note that this architecture is fixed, you can't repatch
things. Of course, with this simple setup little repatching is
necessary. All reasonable connections exist, and you can turn
some off if you don't want them.

Some instruments do allow limited patching- they give you a
choice of destinations for various controls, or have a "patch
cord" list which matches sources to destinations.

Instrument Level Processing

Marketing directors discovered very early on that including
a reverb in a synthesizer would boost sales tremendously. This
follows Elsea's first law of music merchandising "The instrument
that is easiest to play and sounds best in the music store
is the one that sells." A synthesizer sound always benefits
from reverb, even if it's not very good. So, almost all instruments
now include reverb. And while they were at it, the companies threw
in delay and panning and anything else cheap and cute. These effects
are applied to the mixed output of all the voices that are playing.
If you can afford it, you will want to turn these off and use
better quality outboard devices.

MIDI Control

Any digital synthesizer is going to conform to the expectations
of MIDI. A few will outperform MIDI when played by their own keyboard,
but most have descended to the lowest common denominator of the
MIDI standard. Of course, not all instruments implement the same
aspects of MIDI. All respond to notes with the proper pitch and
most have the potential to react to velocity (although this will
change from program to program within the machine), but other
commands cannot be taken for granted. Study of the MIDI implementation
table in the back of the manual is essential before buying an
instrument.

The actual working of MIDI control is pretty straightforward.
When a note on message is received, the synthesizer will begin
playing a note according to its parameter settings and whatever
other MIDI messages have been received to date. Some aspects of
the note may be changed by incoming MIDI data as the note plays,
and the note will go into its completion cycle (envelope release,
etc.) when a note off comes in.

Programs

The sound you get out of a synthesizer is determined by the
values used for all of the subroutines in the processing loop.
These values are known as parameters, and even a simple instrument
will have over a hundred of them. A complete collection of the
parameters is known variously as a program, patch or voice, depending
on the manufacturer. In any case, programming a synthesizer means
adjusting the parameters to get a sound you like. The program
can then be stored in a bank of memory and recalled by a MIDI
message.

Optionally, programs can be stored on data cards, memory cartridges,
cassette tape, floppy disks, or send out via MIDI to another synthesizer
or a computer.

According to Elsea's law, all of the memory banks will have
programs in them when you buy the machine[1].
Since merchandising studies show that few musicians actually program
their synthesizers, many of an instrument's stock programs will
be in (cheap) read only memory.

The User Interface.

Most instruments are modal, with three or four distinct operations.
When you change modes, most of the buttons take on new meanings
(these are often indicated by color coded labels). Typical modes
are:

Play one channel at a time with one voice

Play a lot of channels with different voices(Multi play)

Edit the voices

Edit Multi play setups

Change the behavior of the instrument.

The last category can include such things as tuning, MIDI channels
received and transmitted, maybe the viewing angle of the display.
This kind of information is remembered when the power goes off,
so anything you change will be a surprise to the next user!

SAVING

Most instruments work in a manner similar to computer applications,
where you can call up a document and make changes in it, but the
changes will not be permanent until they are saved. Programs are
not saved to a disk however, they are saved in a battery operated
memory bank. (On some instruments, or with the help of a computer
based librarian, entire banks can be saved onto disks.) You don't
have to save them in the same place they came from, the save procedure
will always give you a chance to pick the destination.

Generally, changing edited programs without saving will result
in the loss of all changes.

EDITING

Originally, digital synthesizers had one knob per parameter,
just like the analog machines. By the second generation, manufacturers
had decided that since you only turn one knob at a time, only
one was necessary[2], along
with a digital display that told you what you were changing. (So
much for unconventional ways of playing.) This means you can't
just grab and twiddle, you must navigate a complex maze of menus,
pages and submenus, and study the manual to see if what you are
about to do will have any effect. Maybe that's why customers quit
programming the things.

The displays are typically organized in groups, and each display
may contain several items. Here is part of the Yamaha SY-35 setup:

In this case, you get to a group such as Voice Common
by pushing a button[3], which
leaves one of the displays showing. A display may have one to
10 items in it. Somewhere in the display is a cursor that shows
what will change when you press the data increment or decrement
buttons. There are other buttons to move the cursor. (You change
displays by getting the cursor under the display name and changing
that.)

Sometimes, a function may apply to one of several similar parts
of the voice. For instance Element Tone: Wave Type display really
looks like this:

There are four tones to this voice: A,B,C and D. One of those
letters in the display will be highlighted, indicating which tone
you are adjusting. There are buttons to push to change this.

Sometimes menus will have submenus. On the Yamaha TX-81 you'll
see a question like

EDIT EG?

and if you hit the YES button, you will descend one more level.
Once you have stepped through all of the options of the envelope
generator you will be returned to the upper level.

Relief is in Sight

More recent (and more expensive) instruments have larger displays
that behave much like Windows dialogs. There will be a few buttons
under the display, and the function of the buttons is indicated
in the display itself. Some new machines now feature calculator
style keypads for entering data, and there is at least one new
instrument with a touch sensitive display, and another that allows
you to plug in a PC type keyboard.